Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
Correct Answer
$6858
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5400 × 3% × 9
= $5400 ×3/100 × 9
= 5400 × 3 × 9/100
= 16200 × 9/100
= 145800/100
= $1458
Thus, Simple Interest = $1458
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 9)
= $5400 + ($5400 ×3/100 × 9)
= $5400 + (5400 × 3 × 9/100)
= $5400 + (16200 × 9/100)
= $5400 + (145800/100)
= $5400 + $1458 = $6858
Thus, Amount (A) to be paid = $6858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $162 × 9 = $1458
Thus, Simple Interest (SI) = $1458
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Similar Questions
(1) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?